Finite Group DatabasebetaFinite Group DatabasebetaOrder 24448.
452 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #27132742 | C2 | semidirect |
| 3. #27132740 | C2 | semidirect |
| 4. #27132716 | C2 | semidirect |
| 5. #27132625 | C2 | semidirect |
| 6. #431×C191 | C2 | semidirect |
| 9. C2×#15690270 | C22 | semidirect |
| 16. C4⋊(C191⋊C8) | C22 | semidirect |
| 18. (C2×D191)⋊C8 | C22 | semidirect |
| 19. C4×C191⋊C8 | C22 | semidirect |
| 21. C4⋊C8×C191 | C22 | semidirect |
| 23. C4×C8×C191 | C22 | semidirect |
| 60. C2×C4×C191 | M16 | semidirect |
| 88. C191 | #2975 | semidirect |
| 94. #431 | D191 | semidirect |
| 107. C4⋊C8 | C2×D191 | semidirect |
| 112. C4×C8 | C2×D191 | semidirect |
| 148. C2×C4 | #15690270 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D764 | 2 |
| #27132742 | 2 |
| #27132740 | 2 |
| #27132716 | 2 |
| #27132625 | 2 |
| #431×C191 | 2 |
| #2975 | 191 |